Learning Control-Oriented Dynamical Structure from Data

TL;DR

This paper introduces a data-driven method to learn a control-oriented factorization of nonlinear dynamical systems, enabling stable trajectory tracking via a state-dependent Riccati equation approach.

Contribution

It presents a novel approach to learn the nonlinear factorization from data, facilitating control synthesis for complex systems without relying on known structure.

Findings

Learned controllers achieve stable trajectory tracking in simulated systems.

The proposed method outperforms recent joint learning approaches in stability.

The factorization learning is effective under mild smoothness assumptions.

Abstract

Even for known nonlinear dynamical systems, feedback controller synthesis is a difficult problem that often requires leveraging the particular structure of the dynamics to induce a stable closed-loop system. For general nonlinear models, including those fit to data, there may not be enough known structure to reliably synthesize a stabilizing feedback controller. In this paper, we discuss a state-dependent nonlinear tracking controller formulation based on a state-dependent Riccati equation for general nonlinear control-affine systems. This formulation depends on a nonlinear factorization of the system of vector fields defining the control-affine dynamics, which always exists under mild smoothness assumptions. We propose a method for learning this factorization from a finite set of data. On a variety of simulated nonlinear dynamical systems, we empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking. Alongside our learning method, we evaluate recent ideas in jointly learning a controller and stabilizability certificate for known dynamical systems; we show experimentally that such methods can be frail in comparison.